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Math: The missing dollar math
Old 01-14-2010, 09:31 AM   #1
themuzicman
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Three men check into an inn. The innkeeper charges them $10 each for one room. The men go to their room. The innkeeper then feels a bit guilty for charging them so much, so he grabs $5, and tells the bellhop to return the $5 to the men. The bellhop, having been stiffed for a tip by these men, reasons that it will be easier for each of them to split $3 rather than $5, so he gives the men $3, and pockets $2.

Now, the men have paid $9 each for the room, having had a dollar returned to them.

Thus, $9 * 3 = $27. The bellhop kept $2. That's $29. Where's the last dollar?
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Old 01-14-2010, 09:34 AM   #2
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25 + 2 = 27

(But I enjoyed the illusion during the double-take)
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Old 01-14-2010, 10:05 AM   #3
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"Now the men have paid $9 each for the room" -- no, the men paid $25 (together) plus a $2 tip, for a total of $27, and they have $3, for a total of $25 + $2 + $3 = $30.

Alternatively: the men paid $9 each for the room ($25) plus tip ($2), for $27 total, and have $3 left over ($27 + $3 = $30).

More importantly, why are three men sharing a hotel room?

(not that there's anything wrong with that ;-)
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Old 01-14-2010, 11:53 AM   #4
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  Originally Posted by themuzicman
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Three men check into an inn. The innkeeper charges them $10 each for one room. The men go to their room. The innkeeper then feels a bit guilty for charging them so much, so he grabs $5, and tells the bellhop to return the $5 to the men. The bellhop, having been stiffed for a tip by these men, reasons that it will be easier for each of them to split $3 rather than $5, so he gives the men $3, and pockets $2.

Now, the men have paid $9 each for the room, having had a dollar returned to them.

Thus, $9 * 3 = $27. The bellhop kept $2. That's $29. Where's the last dollar?

The innkeeper has 25, each men now have 1 dollar (3 between them) and the bellhop has 2.
25+3+2=30

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Old 01-15-2010, 06:17 AM   #5
themuzicman
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But no one has explained why my method is wrong. Effectively, after having received $1 back, each man paid $9 for his room. That's $27. The bellhop has two.

(Part of the answer is to explain why my methodology is wrong.)
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Old 01-15-2010, 06:56 AM   #6
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  Originally Posted by themuzicman
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But no one has explained why my method is wrong. Effectively, after having received $1 back, each man paid $9 for his room. That's $27. The bellhop has two.

(Part of the answer is to explain why my methodology is wrong.)

The 2$ the bellhop has is already contained within the 27$. You don't need to add it on again. 27 + the missing 1 for reach payment = 30.

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Old 01-15-2010, 01:26 PM   #7
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The actually paid 8.33 for the room. Cost of the room is 25 dollars split 3 ways. Then, the belhop keeps 2 dollars (27 total) and they each get refunded a dollar (30 total, or 9.33 each)
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Old 01-15-2010, 01:33 PM   #8
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  Originally Posted by Doppelbock
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More importantly, why are three men sharing a hotel room?

It's Spring Break, they need money for beer.

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